Four roads form a square ACDE with side length s. A barn B is 5 miles from A, 8 miles from C, and 13 miles from D. What is the shortest distance from the barn to the nearest road?
By rotating ∆ABC, we can create an isosceles right triangle with sides 8, 8, 8√2.
Recall that the law of cosines states:
After some calculations, the following measurements can be determined:
Therefore, the distance from the barn to road AC is approximately 1 mile.